# Calculus

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What is the largest rectangle that can be inscribed in the first quadrant of the ellipse 9x^2+16y^2=144?

• Calculus -

base along x-axis, height along y-axis, bottom left vertex at (0,0).
let the top right vertex be (x,y)
from equation
y = (1/4)√(144 - 9x^2)

Area = xy
= x(1/4)√(144 - 9x^2)
differentiate using the product rule, set the derivative equal to zero and solve for x
I got x = 4√3/3 for a max area of 384√3/3

but check my arithmetic.

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